https://orcid.org/0000-0001-5476-9374
ABSTRACT
Urban water distribution networks (WDNs) are facing serious leakage problems. As cities expand, the leakage localization burden on large WDNs gradually increases. Although methods have been widely researched, there is a lack of studies and successful applications for large-scale WDNs. To deal with this, a stepwise fast leakage localization Method, SFLLM, utilizing the `dynamic area narrowing down (DAND)' strategy and coupled leakage features (CLF) is proposed. The SFLLM includes a fast-and-dynamic stage using the DAND strategy to reduce the potential leakage area and an accurate localization stage. Only partial representative candidate locations are required to simulate leakages by DAND, and meantime CLF is used to analyze the leakage similarities so that the localization accuracy and efficiency can be improved. SFLLM was tested on a benchmark WDN, saving more than 88% of simulation by DAND strategy and achieving localization in 11 seconds. The results also proved the enhanced performance of CLF in ensuring the stability of the accuracy against various types of uncertainties that may occur in real WDNs. Moreover, three real burst leaks in an actual large-scale WDN were localized within 205 m in about 22 minutes by SFLLM, showing the method's reliable applicability in guiding field leak exploration.
HIGHLIGHTS
The method proposed is to locate leakages in large-scale water distribution networks (WDNs).
A strategy of dynamic area narrowing down developed to speed up leakage localization.
Utilizing coupled leakage features allows increased accuracy and robustness.
Real burst leaks were localized within 205 m from actual positions in a large-scale WDN of 1,014 km.
INTRODUCTION
The water distribution network (WDN) is indispensable in the entire water supply system for delivering purified water to consumers with adequate quantity, pressure, and quality. However, while fresh water is becoming scarce, it cannot be ignored that the yearly world's non-revenue water (NRW) is around 126 billion cubic meters, accounting for 30% of total water input (Liemberger & Wyatt 2018). Besides commercial losses, WDN leakage is a significant contributor to NRW (Bozkurt et al. 2022), which includes background leakages (Vrachimis et al. 2022) and burst leaks (Huang et al. 2020). Both types of leakage can result in energy and water loss, while broken pipes also threaten water quality, thus hampering the reliable supply and sustainable development of urban water resources (Wang et al. 2022; Marsili et al. 2023). Burst leaks, in particular, generally can be easier to detect and locate than background leakages for the more substantial flow rate and more significant effect on water supply pressure. Accordingly, existing leakage localization methods mainly concentrated on burst leaks, and the ‘leakages’ appearing below will refer specifically to burst leaks unless otherwise noted.
In recent years, a series of studies have been conducted to deal with leakage detection and localization problems in WDNs which can be classified into two main categories: field-equipment-based and remote-sensor-based (Li et al. 2022). Of these, field-equipment-based methods generally offer higher localization accuracy but require specialized hardware equipment to operate in the field, resulting in more expensive costs (Alves et al. 2021). Therefore, these methods are better suited for accurately finding leakage points on burst pipes in a limited range of WDN after remote-sensor-based methods have provided a rough estimate of the possible area.
The remote-sensor-based methodologies can be classified as transient-based (Covas & Ramos 2010), optimization-based (Nasirian et al. 2013; Sophocleous et al. 2019), and data-driven methods, among which data-driven methods have gained significant traction and have been widely studied in the past decade due to the advancements in artificial intelligence technology (Zhou et al. 2019) and the development of real-time data monitoring systems such as supervisory control and data acquisition (SCADA) systems and advanced metering infrastructure (AMI) (Gomathy et al. 2021). In order to achieve localization for burst leaks, proposed methodologies nowadays are more or less developed and assisted by the hydraulic model of WDN (Romero et al. 2021) that is used to obtain network topology or sufficiently simulate leak/leak-free scenarios. For example, Ares-Milián et al. (2021) formulated a two-phase methodology combining a support vector machine multiclass classifier and topological differential evolution based on hydraulic simulation so that the leakage zone can be located with higher performance even for a scenario under considerable demand uncertainty.
Until now, existing leakage localization methods have been successfully confirmed in several hypothetical WDNs (Rolle et al. 2022), highly simplified benchmark networks (Momeni et al. 2022; van Lagen et al. 2022), semi-real (real networks with simulated observations) (Sophocleous et al. 2019; Mashhadi et al. 2021; Alves et al. 2022; Li et al. 2022), and real (real networks with real observations) case studies (Sophocleous et al. 2019; Huang et al. 2020). However, for the WDN of a city with a population of more than 500,000, defined as a large-scale water distribution network (LWDN) in this paper, there is a lack of research and successful application of leakage localization due to the limitation of the large and complex hydraulic model. Although the applied WDN scale of leak localization can be effectively reduced by constructing district metered areas (DMAs) (Huang et al. 2020; Soldevila et al. 2022) for LWDNs, the full establishment of DMAs for an LWDN can take years, and the method may not be feasible during the initial establishment stages due to the deficiency of equipment installation and management system construction. Therefore, with the population served by LWDN expected to rise from 28.7% of the total world population in 2018 to 33.6% in 2030 (United Nations 2019), there is an urgent need for fast leakage localization technology to ensure a higher level of safety operation management.
A stepwise fast leakage localization method (SFLLM) with the dynamic area narrowing down (DAND) strategy is proposed in this paper, focusing on leakage localization in LWDNs or giant DMAs that are larger than regular sizes. Compared with the existing methods, this approach (1) achieves accurate leakage localization in LWDN in a short time, including determining the possible leakage area and identifying the top probable leakage pipe in the reduced area; (2) considers all kinds of errors such as model uncertainties, monitoring noise, and prediction error, and takes into account the influence of different densities of pressure meters in the case study; and (3) has been validated by locating an actual burst event and two pipe flushing events in a real LWDN, demonstrating practical applicability and promising application prospects.
METHODOLOGY
Overview
The structure for the SFLLM consists of two main stages and a functional data preparation section. First, the authentic leakage signal (ALS) is constructed, and the initial candidate leakage area (initial CLA) is selected based on leakage flow rate estimation in the preparation section. Then, in main stage 1, the DAND strategy is employed to dynamically and rapidly reduce the initial CLA to a small region with a high leakage probability, referred to as the final potential leakage area (the final PLA). ‘Dynamically’ means that each CLA formed is unique according to the actual leakage event rather than a pre-defined area. The preliminary planning for the on-site exploration can then commence according to the final PLA.
The framework of the SFLLM.
Data preparation in the fine-established monitoring and management system
SFLLM is developed based on the well-established monitoring and management system (MMS). For a WDN, the well-established MMS means that the hydraulic model has been properly calibrated for the normal/abnormal hydraulic simulation; the monitoring data from the SCADA system are valid; and the historical data are sufficient to build data prediction and leak detection models so that unexpected burst leaks can be detected in a timely manner. Before the main stages, the MMS is utilized to (1) detect the occurrence of the burst leak; (2) pretreat pressure and flow data; (3) estimate the leakage flow rate; (4) determine the initial CLA; and (5) construct the ALS of the burst leak. This paper focuses on the implementation of the last three functionalities, while techniques for data processing and prediction (Chen et al. 2022) and leakage detection (Xu et al. 2020) have already been widely researched, and dependable application modules have been established.
- Estimating the leakage flow rate: The leakage flow rate,
, can be estimated according to the following formula.where(1)
is the overall water consumption when leakage occurs according to monitoring data, and 
is the predicted leak-free overall water consumption by MMS when leakage occurs. - Determining the initial CLA: Due to the fact that burst leaks can occur at any point along a pipeline (Quiñones-Grueiro et al. 2021), only pipe leakages are studied in this paper. For small leakage, it can occur in any pipes, so initial CLA concludes all the pipes in the WDN; while for larger leakages, they can only occur at pipes with larger diameters. On this occasion, the initial CLA is defined as a set of pipes with a diameter larger than the minimal leakable diameter,
. Pipes with diameters smaller than 
will be removed from the initial CLA to speed up the calculation. 
can be calculated aswhere(2)
is the orifice area of the leakage calculated by the orifice outflow equation, and 
is the accepted maximum proportion of the cross-sectional area of the pipe diameter. 
is set to 1 in this study, beyond which the pipe is considered completely broken, which is nearly impossible. This setting helps prevent the accidental deletion of the actual leakage pipe during the CLA initialization to the greatest extent possible. - Constructing the ALS of the burst leak: The leakage signal consists of the absolute value of pressure (AP) when the leakage occurs and the pressure residual (PR) due to the leakage. Therefore, the AP and PR for ALS is
, and 
. 
can be obtained directly from the pretreated monitoring data, and 
is defined aswhere(3)
is the predicted leak-free pressure when the leakage occurs.
Stage 1: dynamically stepwise reduction of potential leakage area
Previous research has primarily relied on generating a large dataset of leakage characteristics for all candidate locations to achieve precise localization results (Zhou et al. 2019; Momeni et al. 2022). However, the hydraulic simulation required for LWDNs is time-consuming and thus can be a bottleneck for such an approach, making it impractical in the real world. The DAND strategy is proposed in this study to overcome this challenge. It achieves fast and effective area reduction of potential leakage area for LWDNs by creating a cyclic searching body, and the procedure is summarized below (regard the initial CLA, the ALS, and 
as input):
Step 1: If this is the start of the search, the current CLA will be the initial CLA. Otherwise, the current CLA will be the updated CLA obtained in Step 6.
Step 2: Group the current CLA temporarily according to the WDN topology and select a representative center position (CP) for each group (sub-CLA).
Step 3: Simulate the leakage scenario on CPs only and calculate the corresponding simulated leakage signal (SLS).
Step 4: Calculate and rank the similarity degree index (SDI) between the SLS of CPs and ALS. SLS of locations within the same group are considered to be closely related. Thus, the SLS of the CP is used to represent the entire group but with approximation errors introduced.
Step 5: Reduce and update CLA by selecting CPs and their corresponding groups based on the SDI ranking. In order to rectify the error introduced in step 4, multiple groups with higher SDI instead of only the top group are selected to update the CLA. This effectively prevents the premature removal of the real leak site that is not grouped in the top group due to interference from monitoring noise, grouping, and CP selection, hence ensuring the coverage of the actual locations in the final PLA.
Step 6: If the proportion of candidate pipes in the updated CLA to the total pipe is less than the predetermined value (the Maximum pipe retention ratio, MPRR), finish the search in stage 1 and obtain the final PLA, otherwise Steps 1–6 are repeated.
In this procedure, parameters that need to be pre-set include the group number (GN) (step 2), the proportion of groups retained for CLA updates, referred to as the group retention ratio (GRR) (step 5), and the MPRR (step 6).
A simple example of the DAND strategy and the construction of temporary sub-CLAs.
A simple example of the DAND strategy and the construction of temporary sub-CLAs.
The construction of temporary sub-CLAs
is the CP for sub-CLA i, 
is the location of pipe j, which is the coordinate of the midpoint of the pipe; N is the number of the candidate pipes in sub-CLA i; and 
is the centroid of the sub-CLA i that can be calculated as Equation (5). Figure 2 illustrates the construction of temporary sub-CLAs and the CP selection in each iteration.
Coupled leakage features
In this study, CLA update is achieved by comparing the SDI between SLS and ALS. As PR correlates more strongly with the leakage than AP and cosine similarity is less impacted by leakage flow rate estimation error, previous studies have preferred using PR over AP to assess leakage similarity between simulated and authentic leakages (Alves et al. 2022; Huang et al. 2022; Yu et al. 2023). However, relying solely on PR may be insufficient in practical applications for the following two reasons: First, significant pressure residuals may not be produced at locations close to the water source, and using these slight pressure residuals for calculation sometimes results in large localization deviations. Second, pressure meters are arranged less densely in actual WDNs than in experimental WDNs, necessitating additional information to improve analysis accuracy.
, and the simulated PR, 
, respectively. And 
is expressed as
and 
are the simulated pressures before and after introducing the leakage at pipe i, respectively. The cosine similarity, 
, and the Euclidian similarity, 
, for candidate pipe i are employed to calculate the SDI for the PR and the AP by the following equations, respectively.
and 
can be calculated, and the total SDI can then be obtained as:
and 
are the coupling ratios of 
and 
, respectively, and satisfy 
.Stage 2: accurate localization of the leakage
Once the candidate pipes in the CLA are reduced to meet the MPRR requirement, the final PLA is obtained, and the leakage scenario will be simulated individually for all candidate pipes within the final PLA in stage 2. Thus, a lower MPRR allows a faster stage 2. However, it can also impact the leakage coverage ability of the final PLA, so in actual practice, determining MPRR is a tradeoff between accuracy and computation time.
The SDIs are then calculated and ranked, and the pipe with the highest SDI value (the Top 1 pipe) is considered the most likely location of the leakage event. This ranking system can also act as an indicator of the likelihood of leakage, which can guide the search sequence for field exploration.
Simulation of the leakage
In this paper, burst leaks on pipes are simulated by directly adding the leakage flow rate in the nodal demand of the new adding node in the middle of the pipe. Although pressure-driven analysis (PDA) provides a more accurate depiction of pressure-deficient conditions under pipe bursts (Yan et al. 2019), the demand-driven analysis (DDA) was adopted mainly beacause PDA necessitates repeated trial calculations for balance to obtain leakage scenarios with specific flow rates, leading to high computational costs for LWDNs. Besides, for the overall pressure data structure used to calculate coupling leakage features, replacing PDA with DDA has an acceptable impact on the results.
Performance evaluation
Three types of metrics are adopted to achieve an overall performance evaluation:
- Accuracy: topological distance (
) between the localized Top1 pipe (
) and the authentic leaky pipe (
). 
is total pipe length of the shortest path from 
to 
:where(10)
and 
are the pipe length of 
and 
, respectively; and 
is the total length of the shortest path between the connection node of 
and the connection node of 
searched by the Dijkstra algorithm (Dijkstra 1959). Efficiency: the total localization time (
).Applicability: the percentage of the successfully located authentic leakage pipe in the final PLA when considering noise for multiple localization,
. Higher 
under a smaller 
means that the original burst position can be more possibly successfully locked in a smaller area, allowing for more reliable guidance on finding and repairing bursts in the field.
RESULTS AND DISCUSSION
The SFLLM was applied in a benchmark WDN, the L-Town (Vrachimis et al. 2022), and a real LWDN, the QD area. The first case employed simulated observations to discuss the parameter selection for the DAND strategy (task 1), demonstrate the performance improvement achieved by using CLF under various integrated noise levels (task 2) and validate the method robustness under different leakage magnitude levels (task 3). In the second case, the method's applicability to real LWDNs was demonstrated by using actual field data from a burst leak event and two pipe flushing events. All experiments were conducted on a desktop computer equipped with an INTEL CORE i7-9700 CPU @ 3.00 GHz, 16 GB of RAM, and a Windows 10 Home 64-bit operating system.
Case study 1: L-town
Detailed information of L-town and QD area
| L-Town | QD area | ||
|---|---|---|---|
| Pipe length | Pipe diameter  100 mm | 8.9 km | 938 km |
Pipe diameter  500 mm | 0 km | 168 km | |
| Total pipe | 42.6 km | 1,014 km | |
| Pipe diameters | 60–225 mm | 25–2,000 mm | |
| Area (km2) | 2.1 | 115.8 | |
| Inlet of WDN | 2 reservoirs | 1 water plant and 4 boundary connections with other regions | |
| Water supply per day | 3,300 tons | 132,000 tons | |
| Population supplied | 10,000 consumers and industries | Around 570,000 residents | |
| Topology of hydraulic model | Number of nodes | 782 | 54,878 |
| Number of pipes | 905 | 42,677 | |
| Number of links | 3 | 12,993 | |
| L-Town | QD area | ||
|---|---|---|---|
| Pipe length | Pipe diameter 100 mm | 8.9 km | 938 km |
| Pipe diameter 500 mm | 0 km | 168 km | |
| Total pipe | 42.6 km | 1,014 km | |
| Pipe diameters | 60–225 mm | 25–2,000 mm | |
| Area (km2) | 2.1 | 115.8 | |
| Inlet of WDN | 2 reservoirs | 1 water plant and 4 boundary connections with other regions | |
| Water supply per day | 3,300 tons | 132,000 tons | |
| Population supplied | 10,000 consumers and industries | Around 570,000 residents | |
| Topology of hydraulic model | Number of nodes | 782 | 54,878 |
| Number of pipes | 905 | 42,677 | |
| Number of links | 3 | 12,993 | |
The topology and partial properties of the hydraulic model of L-Town (a) and QD area (c) and the pipes and the pressure meter selected for L-Town (b).
The topology and partial properties of the hydraulic model of L-Town (a) and QD area (c) and the pipes and the pressure meter selected for L-Town (b).
Model uncertainties and monitoring noise
The proposed approach is a data and model coupling-driven type of method whose performance can be impacted by both monitoring noise in data (MN) and uncertainties in hydraulic model parameters (MU). MN mainly originates from the pressure meters, while the main MU are the nodal demands (NDs) and the pipe roughness coefficients (RCs) (Hutton Christopher et al. 2014). In most previous studies on leakage localization, MN and MU were not fully considered (e.g., not all (Huang et al. 2020; Momeni et al. 2022), only MN (Sophocleous et al. 2019), or only MU (Zhou et al. 2019)), making the results incomparable and lacking practical guidance. Therefore, this paper comprehensively assesses the applicability of SFLLM by considering three integrated noise levels, including both MN and MU, that exist in real-world scenarios. Furthermore, the estimation error of the leakage flow rate introduced from the prediction error of 
in MMS is also taken into account. In this study, the integrated noise level was designed as three scales (NL-1, NL-2, and NL-3) with the specific values shown in Table 2.
The types of noise introduced and the range of their values
| Type | The variable | Probability distribution type | Value range |
|---|---|---|---|
Uncertainties of the hydraulic model ( ) | Uncertainty of pipe roughness coefficient (RCs) | Uniform distribution  |  for the NL-1, NL-2, and NL-3, respectively |
| Uncertainty of nodal demands (NDs) | Uniform distribution  |  for NL-1, NL-2, and NL-3, respectively | |
| Monitoring noise | Monitoring noise of pressure sensors ( ) | Uniform distribution  |  for NL-1, NL-2, and NL-3, respectively |
| Prediction error | The prediction error of the water demand forecast model ( ) | Gaussian distribution  |   ,where D is the predicted water demand. |
| Type | The variable | Probability distribution type | Value range |
|---|---|---|---|
| Uncertainties of the hydraulic model () | Uncertainty of pipe roughness coefficient (RCs) | Uniform distribution | for the NL-1, NL-2, and NL-3, respectively |
| Uncertainty of nodal demands (NDs) | Uniform distribution | for NL-1, NL-2, and NL-3, respectively | |
| Monitoring noise | Monitoring noise of pressure sensors () | Uniform distribution | for NL-1, NL-2, and NL-3, respectively |
| Prediction error | The prediction error of the water demand forecast model () | Gaussian distribution | , where D is the predicted water demand. |
Note:1According to the research of Pu et al. (2022), the best-forecasted value of Mean Absolute Percentage Error (MAPE) of the forecast model is 1.25% (15 min).
Experimental design
In addition to the integrated noise, the experimental design for case 1 is as follows:
The selection of leakage pipes: A total of 50 representative pipes were selected considering the distribution of location and diameter to simulate various burst leak events, as shown in Figure 3(b).
The number of pressure meters selected: 29 pressure gauges are installed in Area A, taking up 4.2% of all nodes. Considering that it is challenging to achieve such high monitoring density in LWDNs, 5 combinations of pressure meter arrangements consisting of 5/10/15/20/29 sensors from existing sensors are selected, as shown in Figure 3(b), to evaluate SFLLM under different pressure monitoring densities.
The number of samples simulated per pipe: Considering integrated noise and estimation error, one leakage event is simulated and located by SFLLM five times per pipe. Then the overall performance, average TD (ATD), average LT (ALT), and CR can be calculated.
The leakage level (
): In tasks 1 and 2, fixed leakage flowrate being 30 cubic meter per hour (CMH) is selected and in task 3, the leakage flowrate is divided into six levels with the mean value being 8/16/32/48/64/80 CMH, referred to as leakage level 1 (LL1) to leakage level 6 (LL6).The MPRR. MPRR was set at 5% for tasks 1 and 2, and varying from 2 to 10% for task 3 to discuss the effects on the localization accuracy.
Simulation duration: 15 min.
Task 1: parameter selection for DAND strategy
The localization results with different parameter values under two situations.
In the analysis of the two aforementioned situations, it is evident that maintaining the GRR at a minimum threshold of 40% stabilizes the overall localization effect, rendering it relatively insensitive to variations in the GN. Furthermore, given that the computational load (the number of leak simulations required for localization, as shown in Figure 4(c) and 4(f)) increases with higher GRR, an optimal balance between localization efficiency and accuracy appears to be achievable when the GRR is set at 40%. Consequently, within this parameter setting, the ideal GN is determined to be ten. This configuration optimizes the tradeoff between computational demand and localization performance.
The application of the DAND strategy yields notable improvements in positioning accuracy, coupled with a substantial reduction in hydraulic computation to approximately 11% of that required by the direct method, provided suitable parameter values are employed. This enhancement can be attributed to the tendency of the direct method to generate false positives stemming from noise-induced perturbations, wherein leakage simulation across all candidate pipes often leads to a high SDI for erroneous locations. Conversely, the DAND strategy, as proposed, directs attention toward areas exhibiting heightened probability, as opposed to individual locations. This targeted approach effectively mitigates interference from noisy data points, rendering the SFLLM well-suited for deployment in real-world LWDNs characterized by diverse uncertainties and noise profiles.
Task 2: The performance improvement by using CLF
The performance by using only PR and CLF under different integrated noise levels.
The performance by using only PR and CLF under different integrated noise levels.
The results depicted in Figure 5 illustrate a direct correlation between the number of monitoring points involved in the calculation, localization time, and localization accuracy, wherein an increase in monitoring points leads to both increased accuracy and time. Notably, when an adequate number of monitoring points (S29) are deployed, the localization accuracy (ATD and CR) remains similar for both types of leakage features. However, as monitoring density diminishes, the advantages of the CLF gradually become apparent. Specifically, the ATD using CLF at monitoring point numbers of 5, 10, 15, 20, and 29 registers reductions of 67.3, 60.3, 30.8, 10.0, and 2.5 m, respectively, compared to the PR method, accompanied by increases in CR by 9.2, 8.4, 6.1, 2.4, and 0.8%. These findings underscore the enhanced robustness of the method under adverse conditions when employing CLF. Furthermore, while the computation time of CLF is marginally greater than that of PR due to the additional Euclidean distance computations, this incremental increase remains acceptable.
Task 3: The robustness of the method for different leakage levels
The average ATD and CR using the SFLLM for different leakage levels with sensor numbers being 29 and 10.
The average ATD and CR using the SFLLM for different leakage levels with sensor numbers being 29 and 10.
Observations reveal that different MPRRs exert minimal effects on final localization accuracy, primarily impacting the CR, whereby higher MPRRs correspond to larger coverage rates (a larger number of candidate pipes in the final PLA is more likely to cover the real leaky pipes). Notably, the method exhibits stable localization even if the final PLA fails to cover the actual leakage location due to significant noise or a smaller leakage flow rate. Furthermore, Figure 6(c) and 6(f) illustrate that computation time at a 5% MPRR is less than that at a 2% MPRR. This discrepancy arises from the increased DAND searching iterations required to achieve a 2% MPRR in the WDN that comprises 765 candidate pipes, rendering Stage 1 more time-consuming. Given the emphasis on localization accuracy and computational efficiency, the most suitable MPRR is 5% for case 1. Besides, for each MPRR value, it can be observed that the LT is slightly faster for smaller LLs. This is because the initial CLA for any LLs includes all pipelines in Case 1, resulting in similar basic computation times, and for the leakages with small flow rates, the pressure response at some monitoring points is too minimal to participate in the calculation, leading to a reduction in the dimensionality of the pressure data, and consequently, a shorter LT.
Regarding localization results, considering an acceptable ATD within 350 m, effective localization requires leakage flowrate to reach LL2, i.e., 16 CMH (ATD = 325 m) with 29 pressure meters, and LL3, i.e., 32 CMH (ATD = 272 m) with 10 pressure meters. Additionally, coverage capacity increases with escalating leakage levels. In situations with 29 and 10 installed monitoring points, a satisfactory degree (over 80%) of coverage for the final PLA can be attained when the leakage flow rate reaches LL3 and LL4, respectively.
Case study 2: QD area
The LWDN of the QD area is an independent part of a megacity located in eastern China, as depicted in Figure 3(c). In this area, intricate joint scheduling among multiple pumping stations is observed, coupled with the presence of only 17 effective pressure monitoring gauges. This situation poses significant challenges for burst leak localization in the area.
One of the important prerequisites for SFLLM implementation is that a leakage event induces pressure anomalies at monitoring points, which are discernible amidst monitoring noise. Following pre-experimental analysis, in the QD area, leakages with an outflow rate of 200 CMH yield a median average pressure drop of 0.26 m at each monitoring point, deemed the minimum localizable leak size conducive to effective localization using SFLLM in the QD area. Furthermore, in consideration of the prediction error associated with regional water demand, to attain a more satisfactory positioning result, it is recommended that the leakage flow rate of the event exceeds 300 CMH. In this paper, the SFLLM was employed to localize three burst leak events occurring between 2021 and 2022, encompassing one real pipe burst event and two burst-like events stemming from pipe flushing. Detailed information regarding these events is presented in Table 3.
Information and overall localization results of the three burst leak events
| Burst leak (event 1) | Pipe flushing Ⅰ (event 2) | Pipe flushing Ⅱ (event 3) | |||
|---|---|---|---|---|---|
| Event information | Start time | 2,021.4.30 14:30 | 2,022.11.24 22:05 | 2,022.11.24 23:25 | |
| Estimated outflow (CMH) | 1,793 | 611 | 1,149 | ||
| Leakage as a proportion of water demand | 16.24% | 5.49% | 12.05% | ||
| The maximum pressure drop (m) | 11.21 | 1.65 | 1.26 | ||
| Details of localization result | Number of candidate pipes in the final PLA | 171 | 166 | 153 | |
| If the real location is covered by the final PLA | √ | √ | √ | ||
| TD (m) | 176.37 | 112.83 | 204.11 | ||
| LT (min) | Stage 1 | 11.5 | 13.1 | 12.6 | |
| Stage 2 | 8.9 | 8.1 | 7.7 | ||
| Total | 20.4 | 21.2 | 20.3 | ||
| Burst leak (event 1) | Pipe flushing Ⅰ (event 2) | Pipe flushing Ⅱ (event 3) | |||
|---|---|---|---|---|---|
| Event information | Start time | 2,021.4.30 14:30 | 2,022.11.24 22:05 | 2,022.11.24 23:25 | |
| Estimated outflow (CMH) | 1,793 | 611 | 1,149 | ||
| Leakage as a proportion of water demand | 16.24% | 5.49% | 12.05% | ||
| The maximum pressure drop (m) | 11.21 | 1.65 | 1.26 | ||
| Details of localization result | Number of candidate pipes in the final PLA | 171 | 166 | 153 | |
| If the real location is covered by the final PLA | √ | √ | √ | ||
| TD (m) | 176.37 | 112.83 | 204.11 | ||
| LT (min) | Stage 1 | 11.5 | 13.1 | 12.6 | |
| Stage 2 | 8.9 | 8.1 | 7.7 | ||
| Total | 20.4 | 21.2 | 20.3 | ||
The localization results for the pipe burst event (a, b), pipe flushing event Ⅰ (c, d), and the pipe flushing event Ⅱ (e, f) after localization stage 1 and stage 2 of SFLLM, respectively.
The localization results for the pipe burst event (a, b), pipe flushing event Ⅰ (c, d), and the pipe flushing event Ⅱ (e, f) after localization stage 1 and stage 2 of SFLLM, respectively.
Due to the significant leakage flow, certain pipes with diameters smaller than 
were removed during the data preparation stage. Additionally, closed valves were present in the WDN, leading to partial disconnection within the CLA, thereby influencing the sub-CLA grouping results. Consequently, the final PLA in Figure 7(b), 7(d), and 7(f) may exhibit multiple sub-connection areas. Nevertheless, despite these pipe disconnections, the final results remain highly indicative. According to the records provided by the water utility, event 1 occurred at a pipe with a diameter of 500 mm, and events 2 and 3 took place at a DN1000 pipe near a pumping station, where distinguishing leakage amid stable pressure conditions proves challenging. The ATD between the actual location and the Top 1 pipe for these three events measures 176.47, 112.83, and 204.11 m, respectively. Such localization accuracy falls within an acceptable range for an LWDN equipped with only 17 monitoring points, offering effective guidance for burst leak exploration in the field. Detailed localization results are summarized in Table 3.
CONCLUSIONS
This study proposed an SFLLM to address the leakage localization problem in LWDNs. It includes a DAND strategy in stage 1 for quick narrowing down of the possible leakage area (rough but quick) and stage 2 for precise analysis of the probable leakage location (accurate but relatively time-consuming). Combining the two stages allows localization accuracy and efficiency to be effectively balanced and ensured. Besides, the CLF is proposed to enhance the localization stability of the method to cope with various types of unfavorable conditions.
Two case studies were conducted to investigate the accuracy of the proposed SFLLM. Case 1 optimizes the parameters and discusses the method's effectiveness in a benchmark WDN under different integrated noise levels, monitoring point densities, and leakage levels. Results showed that the proposed method can significantly reduce 88% of the number of simulations compared with the direct method with appropriate parameters while ensuring localization accuracy, making it more suitable for practical applications in LWDN. As for L-Town, it took less than 11 s to localize each leak event. The utilization of CLF for analysis proves to be more effective in coping with inadequate pressure gauge arrangements commonly encountered in real-life scenarios. For instance, in situations where the pressure meters arrangement is insufficient (i.e., 5/10/15 pressure gauges installed), the average ATD by employing CLF instead of solely relying on the PR feature for the leakage with a flow rate of 30 CMH across all integrated noise levels reduce by 67.3, 60.3, and 30.8 m, respectively. Simultaneously, the average CR improves by 9.2, 8.4, and 6.10%, respectively.
Moreover, upon analyzing the localization capability for varying leakage levels, it becomes evident that setting different MPRRs primarily affects the ability of the final PLA to cover the actual leak location, with minimal impact on localization accuracy. Consequently, the MPRR can be selected judiciously based on the acceptable calculation time in practical applications. In this study, for both scenarios of adequate and inadequate arrangements of monitoring points, the recommended reliable localization leakage thresholds are LL2 and LL3, with corresponding localization ATD of 325.3 and 272.8 m, respectively.
In Case 2, SFLLM was applied to an actual LWDN, where a real burst event with a large burst flow rate and two pipe flushing events with slightly lower leakage flow rates were analyzed. The proposed method efficiently reduced the candidate pipes by 99.5% and quickly but accurately located the leakages (with TDs being 176.47, 112.83, and 204.11 m, and LTs being 20.4, 21.2, and 20.3 min, respectively), with valuable positioning accuracy and efficiency for an LWDN with pipelines totaling 1,014 km and only 17 validated pressure meters. Deploying the method on high-performance servers will further enhance its positioning speed.
From Case 1 and Case 2, it is evident that SFLLM can effectively address leakage localization problems in WDNs of varying sizes and complexities. However, due to its breakthrough solutions to the challenges of inaccurate positioning and low efficiency in leakage localization for large-scale WDNs, compared to deep learning-based and heuristic search algorithm-based approaches, SFLLM is emphasized in this article as a method for LWDNs. In the previous study, the deep learning-based approach achieved the localization in seconds due to disentangling the data generation and training from the actual localization, but considering the complex and variable operating conditions in LWDNs, the enormous and additional time required for regular re-simulation of the training set and the update of the classification model should also be counted in the time overhead. Taking the method, a burst localization framework based on the fully linear DenseNet, proposed by Zhou et al. (2019), as an example, to achieve the leakage analysis at the level of a single pipe in the whole LWDN as the QD area, a classification model with tens of thousands of classes is required to be constructed, and hundreds of thousands of leakage samples are needed to be simulated, making it challenging to complete such work for practical applications. However, considering that the better robustness of the deep learning classification method is proven in small areas, future work will attempt to couple the DAND strategy with it. As for heuristic-based search methods (Wu et al. 2021; Min Kyoung et al. 2022), it is also inefficient in locating leaks in LWDNs due to their multigenerational search with a large number of populations. It is more suitable for locating complex multiple simultaneous leaks in smaller networks or small leaks that do not require fast localization.
In conclusion, SFLLM is of high practicality for achieving efficient leakage localization in LWDNs that can effectively guide leakage on-field exploration, contributing to the conservation of water resources. As a practical application of this research, an online tool was developed by coupling the localization model based on SFLLM and the detection model proposed by Xu et al. (2020) to serve the water utility of the QD area with good results.
FUNDING
This work was supported by the National Natural Science Foundation of China (Grant No. 52270093, 51978494) and the Shanghai Science and Technology Innovation Action Plan (Grant No.22dz1201800).
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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